The Coupling of Voltage and Frequecncy Response in Splitting Island and Its Effects on Load-shedding Relays

doi:10.4236/epe.2013.54B128

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Energy and Power Engineering, 2013, 5, 661-666

doi:10.4236/epe.2013.54B128 Published Online July 2013 (http://www.scirp.org/journal/epe)

The Coupling of Voltage and Frequecncy Response in

Splitting Island and Its Effects on Load-shedding Relays*

Hao Yang, Baohui Zhang

School of Electrilcal Engineering, Xi’an Jiaotong University, Xi’an, China

Email: [email protected]

Received February, 2013

ABSTRACT

The voltage and frequency dynamics interact with each other in the island after splitting. The current frequency re-

sponse model without considering the voltage effect would bring remarkable errors when analyzing the frequency dy-

namic progress in the island with large-capacity active-power shortage. In this paper, coupling effects of voltage and

frequency are studied to indicate that initial reactive-power deficit and load characteristics have strong effects on the

coupling effects of the voltage and frequency. Moreover, control effects of currently used under frequency load-shed-

ding relays (UFLS) and under voltage load-shedding relays (UVLS) which are installed and executed independently are

examined to find that it would sometimes cause excessive or inadequate control without considering the coupling, sug-

gesting that it is necessary to develop coordinate control methods for voltage and frequency problems.

Keywords: Frequency Response; Coupling Effects; Splitting Island; Coordination Control

1. Introduction

Frequency, voltage and angle stability are three main

kinds of power system stability, respectively [1]. How-

ever, when compared with the other two kinds, frequency

stability has drawn less attention [2]. Currently, power

grids in China has stepped into the age called large

power grids, high voltage and large units[3], the fre-

quency instability risk for the whole grid has decreased,

but the risk for the region grids has increased[4], espe-

cially with the growing amount of renewable energy.

Once the region grids disconnected with the main one

due to splitting accident, currently installed under fre-

quency load-shedding device (UFLS) may fail to ensure

the island frequency stability [5].

At present, the last line of defense ensuring frequency

stability is UFLS, whose setting is commonly based on

single-machine single-load frequency model, ignoring

voltage effects on frequency, such as the system fre-

quency response model (SFR) [6] and average system

frequency model (ASF) [7]. In fact, there are obvious

differences for voltage and frequency at different buses

due to space-time distribution characteristics [8]. How-

ever, there have been few studies about voltage effect on

frequency dynamic. Owing to load characteristics, the

negative effect of load-shedding on frequency recovery

was first reported in [9]. Considering load-voltage ef-

fects，less amount of load can be shed when UFLS per-

forms [10]. Although some researchers have realized the

value of coupling effects on frequency dynamic, the key

factors affecting the interaction and the mechanism have

not been analyzed carefully yet. Furthermore, few studies

have been done on the effect of the coupling on the third

line of defense for power system safety.

In this paper, we will analysis how the coupling affects

the frequency dynamic based on simulations of the con-

ventional system. Our results would help to find the key

factors affecting the interaction. Then the effects of the

coupling on the UVLS and UFLS performance are veri-

fied to indicate that it is necessary to develop the fre-

quency and voltage combined control method.

2. Frequency Changing Characteristic in the

Island

The frequency response is decided by the active-power

balance dynamic on the generator as expressed in equa-

tions (1) - (4), which suggest that the load voltage can

affect the system frequency response through changing

the absorbed active-power of its own :

coi

i mi etotal

eq ii

df PPP

dt 



 (1)

*The work Project Supported by State Grid Corporation of China,

Major Projects on Planning and Operation Control of Large Scale

Grid(SGCC-MPLG030-2 012)

,, ,

ie jlkl

ijLkM

PP P





 (2)

H. YANG, B. H. ZHANG

662



(, ,,)L.

jjjjj

PPUfxt j

(3)

(, ,)(M)

kk k

PgUUy k



 . (4)

where fcoi

，

Pi,m and Pi,e are the system inertia center fre-

quency, the mechanical and electromagnetic power of the

ith generator. Land M donates the load and line collec-

tions. P expresses active-power equation for loads, in

which x is the state variables. G expresses load loss equ-

ations.

The single-machine single-load frequency model im-

plies that the frequency can be predicted only by the in-

tial active-power shortage (ΔP0). This kind of model

agrees well with actual response data whenΔP0 is rela-

tively small. However, in some situations which may

cause large-capacity active-power shortage, for example

when the region grid is spitted from the main one, we

find the conclusions obtained from the conventional

model are quite different from the fact, sometimes even

opposite to the truth.

3. Simulation and Mechanism Analysis

3.1. Simulation Situations Description

The EPRI 36-bus system is as shown in Figure 1 in

which the governors and voltage regulator are carefully

considered, the load was modeled through a composite

model consisting of constant impedance and induction

motor considering rotor mechanical and electromagnetic

transient. All the eight generators adopt 6th –order model,

including governor and voltage regulator. Simulations

were conducted on power system analysis software

(PSASP) developed by China Electric Power Research

Institute (CEPRI), the integration step-size was 0.01 s,

total simulation time was 20 s.

A group of Lines (marked with X) was chosen as split-

ting section which divided the whole system into two

parts. Focus attention on the bottom right area with posi-

tive initial active-power deficit as shown in Figure 2.

Figure 1. EPRI 36-bus system.

To simplify the fault situation, the splitting accident

was simulated by disconnecting the section at 0.2 s.

Maintain the cross-section, effects of reactive-power

transferred through the cross-section and load character-

istics on the island frequency response were researched.

3.2. Effects of the Reactive-power Shortage

In conventional opinions, initial active-power shortage

(ΔP0) affects significantly the frequency response dy-

namic, but initial reactive-power shortage(ΔQ0) slightly

affects the frequency dynamic. However, after further

research we find the change of ΔQ0 has a remarkable

effect on the frequency response through voltage and

frequency coupling. Analyzing frequency without con-

sidering ΔQ0 would bring obvious errors.

Maintain ΔP0 at 6 p.u. (System base capacity is 100

MVA) , the change of ΔQ0 is as shown in Table 1.

Figure 3 shows the voltage curves observed at Node

16.

Figure 2. The sketch map for isolated island after splitting.

Table 1. Initial reactive-power shortage chang conditions.

Power shortage conditions

Conditions Reactive-power

shortage(p.u.)

Percentage in load reac-

tive-power demand

1 0.5 8%

2 1 16%

3 1.25 20%

4 1.4 22.4%

5 1.5 24%

6 1.6 25.6%

7 2 32%

8 2.5 40%

H. YANG, B. H. ZHANG 663

It can be seen from Figure 3 that the voltage decreases

as ΔQ0 increases, which can also be observed at other

buses. From Equations (3) it can be noted that island

voltage affects the total active-power absorbed by loads

(∑PL). From Equations (2) it can be seen that ∑PL is the

major part of the total electromagnetic active-power of

the island(∑Pe). Figure 4 shows the change of ∑Pe with

different ΔQ0:

From Figure 4 it can be observed that ∑Pe decreases

with ΔQ0 increases. When the ΔQ0 increases over a cer-

tain threshold, ∑Pe drops sharply due to the voltage de-

cline.

Meanwhile the change of total mechanical power in

the island (∑Pm) decided by governors at generators is as

shown in Figure 5:

Figure 3. Voltage of Bus 16 under different ΔQ0.

Figure 4. Values of total Pe under different ΔQ0.

Figure 5. Total Pm under different ΔQ0.

The difference between ∑Pm shown in Figure 5 and

∑Pe shown in Figure 4 ,which is called unbalanced ac-

tive-power (ΔPtotal) is shown in Figure 6.

From Equations (1) it can be seen that ΔPtotal decides

the frequency dynamic of the island, which is shown in

Figure 7.

It can be seen from Figure 7 that:

1) Under all conditions, frequency drops at the initial

moment, the dropping rate of frequency decreases when

ΔQ0 increases, but the differences among all of the con-

ditions are slight.

2) Effects of change of ΔQ0 on frequency appears ap-

parently after 0.4 s. When ΔQ0 increases(See Figure 3) ,

voltage decreases ,leading to the decrease of ∑PL due to

voltage effects on the load active-power. Then ∑Pe de-

creases (See Figure 4), causing the increase of ΔPtotal

(See Figure 6). As a result, the frequency decided by

ΔPtotal increases when ΔQ0 increases. If ΔQ0 exceeds a

certain threshold(e.g., 2 p.u.), causing voltage instability

at some load buses, leading sharp drop of ∑PL, whose

decline value can be higher thanΔP0, causing the sign of

ΔPtotal to change ,and then the frequency of the island

would exceed rating value(i.e., 50 Hz) despite of the se-

vere ΔP0.

From above discussions it can be implied that the fre-

quency changing trend cannot be predicted accurately

only byΔP0. ΔQ0 affects the voltage, changing frequency

dynamic. Conclusions without considering ΔQ0 can be

far from, sometimes even inverse to the truth. It is nec-

essary to consider reactive-power balance when analyz-

ing island frequency.

Figure 6. Unbalanced active-power under different ΔQ0.

Figure 7. Frequency response under different ΔQ0.

H. YANG, B. H. ZHANG

664

3.3. Effects of Load Characteristics

Maintain power transferred through the cross-section at

6+j1.5. The load characteristic was varied by changing

the percentage of induction motor in the compositive

load as shown in Table 2.

Figure 8 shows voltage of Bus 16:

It can be seen that the percentage of induction motor

has a remarkable effect on voltage response. When the

percentage increases, voltage decreases .When the per-

centage exceeds 30%, the motor instability happens due

to voltage drop, whose active-power decreases sharply as

well as the reactive-power clearly increases .The change

of motor variables when the percentage is 40% is as

shown in Figure 9.

In Figure 9, V,s,P and Q represent slip ratio, voltage,

active-power, reactive-power of the motor, respectively.

The change of ∑Pe is as shown in Figure 10:

It can be seen From Figure 10 that ∑Pe decreases with

the percentage increases.

The frequency change curves in various situations are

as shown in Figure 11:

ΔPtotal is as shown in Figure 12:

It can be seen that the percentage of induction motor

significantly affects the frequency dynamic through

changing the island voltage. ΔPtotal and frequency in-

crease with the percentage increses. While the percentage

exceeds a certain threshold, the sign of ΔPtotal would

change, causing that frequency of the island exceeds rat-

ing value despite of severe ΔP0.

Table 2. Loda characteristic change in the island.

Load model component

Model Induction motor(%) Constant impedance(%)

1 0 100

2 20 80

3 25 75

4 30 70

5 35 65

6 40 60

7 45 55

Figure 8. Voltage of Bus16 under different load characteristics.

Figure 9. Related variables of the motor at Node 16 under

different load characteristics.

Figure 10. Response curves of total Pe in the isolated island

under different load characteristics.

Figure 11. Response curves of frequency in the isolated is-

land under different load characteristics.

Figure 12. Comparisons of unbalanced active-power in the

isolated island under different load characteristics./

H. YANG, B. H. ZHANG 665

4. Effects of the Coupling on Load –shedding

Devices

4.1. Load-shedding Devices Installed Situations

and Existing Problems

In current China’s power grids underfrequency load-

shedding (UFLS) and undervoltage load-shedding

(UVLS) are two different kinds of devices installed to

prevent frequency and voltage instability, respectively.

However, these two kinds of devices are set and perform

independently despite of the coupling between frequency

and voltage .Lacking the coordination between them

would result in excessive or insufficient control.

The UFLS and UVLS installations adopted in current

Shanxi Province in China are as shown in Table 3 and

Table 4.

The load-shedding devices are both installed at each

load node of the island.

We research control effects of the current load-shed-

ding device on the island with the coupling of voltage

and frequency.

4.2. Control Effects When ΔQ0 Changes

Table 5 shows the control effects with different ΔQ0, the

conditions are just the same as shown in Table 1.

From Table 5 it can be seen that:

1) The total shedding amount carried out by UVLS

and UFLS decrease as ΔQ0 increases.

2) The shedding amount carried out by UVLS in-

creases as ΔQ0, UVLS cannot start When ΔQ0 is less

than a certain threshold.

3) The shedding amount carried out by UFLS in-

creases as ΔQ0 decreases, UFLS cannot start When ΔQ0

is more than a certain threshold.

Table 3. UFLS setup situations.

Setup stages

UFLS

I II III IV V VI VII

fset(Hz) 49 48.8 48.6 48.4 48.2 48 49

Tdelay(s) 0.2 0.2 0.2 0.2 0.2 0.210

Pshed(%) 7 7 7 7 7 7 4

Table 4. UVLS setup situations.

Setup turns

UVLS

I II III IV

Uset(p.u.) 0.85 0.8 0.75 0.85

Tdelay(s) 1 1 1 10

Pshed(%) 7 7 7 4

4) Lack of coordination between UVLS and UFLS

would cause excessive control ( i.e, fmax > 51 Hz) under

some conditions(e.g.,ΔQ0=1,1.5), in which low fre-

quency and low voltage happen at the same time.

5)Currently used load-shedding relays may not prevent

island from collapse under some situations(e.g. ΔQ0 =

2,2.5),in which high frequency and low voltage happen at

the same time, causing that UFLS cannot act and UVLS

is too late to shed insufficient amount of load.

4.3. Control Effects When Load Characteristics

Changes

Table 6 shows the control effects, the conditions are just

the same as shown in Table 2 .

What can be seen From Table 6 are similar to those

obtained from Table 5 :

1) The total shedding amount decreases as the per-

centage of induction motor in load increases.

2) The shedding amount carried out by UVLS in-

creases as the percentage, UVLS cannot start when the

percentage is less than a certain threshold.

3) The shedding amount carried out by UFLS in-

creases as the percentage decreases, UFLS cannot start

when the percentage is more than a certain threshold.

4) Lack of coordinates between UVLS and UFLS

would cause excessive control (i.e, fmax> 51Hz) under

some situations (e.g., the percentage equals 30%), in

Table 5. Control effects when ΔQ0 changes.

Control Effects

Codition 0



(p.u.)

UFLS

(p.u.)

UVLS

(p.u.)

fmax

(Hz)

f∞

(Hz) Umin (p.u)

1 0.5I-IV(4.69)\ 50.89 48.10 0.998

2 1 I-IV(4.69)I ( 0.76 ) 51.21 48.30 0.999

3 1.5I-III(3.52)I,II(1.16) 51.16 48.33 0.943

4 1.6I,II(2.35)I,II(1.88) 50.67 48.55 0.925

5 2 \ I-IV(3.96) 51.59 49.83 0.649

6 2.5\ I-IV(3.99) 52.34 49.94 0.576

For example, I-IV(4.69) means that UFLS performs four steps with 4.69 p.u.

load shed.

Table 6. Control effects with different load characteristic.

Control Effects

Codition Motor

(%)

UFLS

(p.u.)

UVLS

(p.u.)

fmax

(Hz)

f∞

(Hz)

Umin

(p.u)

1 20 I-III(3.52)I(0.76) 50.85 49.760.933

2 25 I-III(3.52)I(0.76) 50.83 48.750.931

3 30 I-III(3.52)I,II(1.16) 51.11 49.990.967

4 35 \ I-IV(3.60) 51.56 50.660.628

5 40 \ I-IV(3.99) 52.35 51.170.606

H. YANG, B. H. ZHANG

666

which low frequency and low voltage happen at the same

time.

5)The present UVLS and UFLS may not prevent is-

land from collapse under some situations(e.g., the per-

centage equals 35% or 40% ),in which high frequency

and low voltage happens at the same time, causing that

UFLS cannot act and UVLS is too late to shed insuffi-

cient amount of load.

5. Conclusions

The island frequency response is decided by both me-

chanical power and electromagnetic power. Island volt-

age affects electromagnetic power, which change the

frequency dynamic in island. Initial reactive-power defi-

cit and load characteristics are two key factors affecting

the frequency response dynamic through coupling of

voltage and frequency when initial active-power main-

tains unchanged.

When initial reactive-power or percentage of induction

motor in loads increases, the voltage decreases, leading

the decrease of total electromagnetic power. As the de-

crease of unbalanced active-power in island, the decrease

of frequency decline rate and the increase of frequency.

While initial reactive-power deficit or percentage of in-

duction motor in load exceeds a certain threshold, the

signal of unbalanced active-power in island would

change, which may cause high frequency despite of se-

vere active-power deficit in the island.

Ignoring the coupling of voltage and frequency dy-

namic would result in remarkable errors when analyzing

the frequency response of the splitting island with large

initial active-power deficit.

Moreover, the currently used UVLS and UFLS, whose

setup and performance are independent without consid-

ering the coupling of voltage and frequency, would cause

excessive when low voltage and low frequency happen at

the same time or insufficient control when initial reac-

tive-power deficit or percentage of induction motor in

load exceeds a certain threshold.

It is necessary to develop coordination control for vol-

tage and frequency on the basis of research on their cou-

pling effects.

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